Complex Expression (x^4)

[wizzl]

Need some help solving this?

=5(1+x^4)-2.5(1+x^3)-2(1+x^2)-1(1+x)-1


Thanks in advance-

 

[stapel]

Is this expression set equal to zero?

Eliz.

 

[wizzl]

yes

 

[stapel]

Well, the first step would be to multiply everything out, simplify, and write in descending order. Then... have you learned about the Rational Roots Test and synthetic division? If so, how far have you gotten with these tools? If not, what method are you supposed to be using for solving?

Thank you.

Eliz.

 

[wizzl]

I actually have shown a simplified version of the original problem. This actually comes from a finance problem where internal rate of return is being calculated for multiple cash flows.

It has been a long time since I had to solve a problem like this. Can you assist?

Thanks again

 

[sco11]

ok so that =
(5x^4)-(2.5x^3)-(2x^2)-(x)-1.5
which =
5(x-1.1726227148)(x+.665852232753)(x^2+.006770482048x+.384224533279)
factored.

But you might just want to work with the top answer.. I don't really know what you are solving for (x?).

 

[Denis]

I actually have shown a simplified version of the original problem. This actually comes from a finance problem where internal rate of return is being calculated for multiple cash flows.
It has been a long time since I had to solve a problem like this. Can you assist? Thanks again

Huh? If that's the case, how in heck did you arrive at a formula/equation
like that one?!
Does x^4 stem from x^n, where n = 4 years...or something similar?
Please post the ORIGINAL problem.

 

[wizzl]

Here's the original problem with solution:

Set the project’s cash flows, discounted at the internal rate of return (IRR), equal
to zero. Solve for the IRR.
IRR = C0 + C1 / (1+IRR) + C2 / (1+IRR)^2 + C3 / (1+IRR)^3

0 = -$600,000+ $270,000 / (1+IRR) + $350,000 / (1+IRR)^2 + $300,000 /
(1+IRR)^3

How do they get to this answer below:

IRR = 0.243
The IRR of the deepwater fishing project is 24.3%.

 

[soroban]

Hello, wizzl!

Now, that's an entirely different equation ... you misplaced all the exponents.

- 600,000 + 270,000/(1 + x) + 350,000/(1 + x)² + 300,000/(1 + x)³ .= .0

Divide through the equation by 10,000
. . and let u = 1 + x.

The equation becomes: .- 60 + 27/u + 35/u² + 30/u³ .= .0

Multiply by -u³: . 60u³ - 27u² - 35u - 30 .= .0

And, somehow, we're expected to solve this cubic equation.

 

[Denis]

Using soroban's MAGNIFICIENT 60u^3 - 27u^2 - 35u - 30 = 0

At least, you can "see" that 1.243 is probably correct:
u=1: left side = -32
u=2: left side = 272

So solution lies between 1 and 2, and closer to 1.